{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 处理文本（数学表达式）"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "在字符串中使用一对 `$$` 符号可以利用 `Tex` 语法打出数学表达式，而且并不需要预先安装 `Tex`。在使用时我们通常加上 `r` 标记表示它是一个原始字符串（raw string）"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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LNOublhHfH70ktyb5VpK5KZc4NSO8P9YkuTbJbV1fnL0CZU5Fkk8luS/JNwe0GS83q2pi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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa0d7518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plain text\n",
    "plt.title('alpha > beta')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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oqn9L8u/AKxndf/N8M3M3531Z5uhNT0lOZXTT0+ofztuA98PRO2CPe9NTAxPXIslLgVuB\n91bVgS2Y46JMXIuqenlVvayqXsbouvtHmoUdpvv5+Efgj5JsS3IaozfPfrDgeS7CNGuxD7gEYHx9\n+ZXADxc6y5PHzN2c65l7edPTUdOsBfBJ4MXADeMz1sNVdeFWzXmzTLkW7U3587EvyR3Ag8DTwE1V\n1S7uU35PfBq4JckDjE5EP1ZVP92ySW+iJF8C3grsSHIQuI7RJbp1d9ObmCSpIf83e5LUkHGXpIaM\nuyQ1ZNwlqSHjLkkNGXdJasi4S1JDxl2SGvp/zy4/4DuVo0MAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa162860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# math text\n",
    "plt.title(r'$\\alpha > \\beta$')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 上下标"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "使用 `_` 和 `^` 表示上下标：\n",
    "\n",
    "$\\alpha_i > \\beta_i$：\n",
    "\n",
    "    r'$\\alpha_i > \\beta_i$'\n",
    "\n",
    "$\\sum\\limits_{i=0}^\\infty x_i$：\n",
    "\n",
    "    r'$\\sum_{i=0}^\\infty x_i$'\n",
    "\n",
    "注：\n",
    "\n",
    "- 希腊字母和特殊符号可以用 '\\ + 对应的名字' 来显示\n",
    "- `{}` 中的内容属于一个部分；要打出花括号是需要使用 `\\{\\}`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 分数，二项式系数，stacked numbers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\frac{3}{4}, \\binom{3}{4}, \\stackrel{3}{4}$：\n",
    "\n",
    "    r'$\\frac{3}{4}, \\binom{3}{4}, \\stackrel{3}{4}$'\n",
    "\n",
    "$\\frac{5 - \\frac{1}{x}}{4}$：\n",
    "\n",
    "    r'$\\frac{5 - \\frac{1}{x}}{4}$'\n",
    "\n",
    "在 Tex 语言中，括号始终是默认的大小，如果要使括号大小与括号内部的大小对应，可以使用 `\\left` 和 `\\right` 选项：\n",
    "\n",
    "$(\\frac{5 - \\frac{1}{x}}{4})$\n",
    "\n",
    "    r'$(\\frac{5 - \\frac{1}{x}}{4})$'\n",
    "\n",
    "$\\left(\\frac{5 - \\frac{1}{x}}{4}\\right)$：\n",
    "\n",
    "    r'$\\left(\\frac{5 - \\frac{1}{x}}{4}\\right)$'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 根号"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\sqrt{2}$：\n",
    "\n",
    "    r'$\\sqrt{2}$'\n",
    "\n",
    "$\\sqrt[3]{x}$：\n",
    "\n",
    "    r'$\\sqrt[3]{x}$'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 特殊字体"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "默认显示的字体是斜体，不过可以使用以下方法显示不同的字体：\n",
    "\n",
    "命令|显示\n",
    "--|--\n",
    "\\mathrm{Roman}|$\\mathrm{Roman}$\n",
    "\\mathit{Italic}|$\\mathit{Italic}$\n",
    "\\mathtt{Typewriter}|$\\mathtt{Typewriter}$\n",
    "\\mathcal{CALLIGRAPHY}|$\\mathcal{CALLIGRAPHY}$\n",
    "\\mathbb{blackboard}|$\\mathbb{blackboard}$\n",
    "\\mathfrak{Fraktur}|$\\mathfrak{Fraktur}$\n",
    "\\mathsf{sansserif}|$\\mathsf{sansserif}$\n",
    "\n",
    "$s(t) = \\mathcal{A}\\ \\sin(2 \\omega t)$：\n",
    "\n",
    "    s(t) = \\mathcal{A}\\ \\sin(2 \\omega t)\n",
    "\n",
    "注：\n",
    "\n",
    "- Tex 语法默认忽略空格，要打出空格使用 `'\\ '`\n",
    "- \\sin 默认显示为 Roman 字体"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 音调"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "命令|结果\n",
    "--|--\n",
    "`\\acute a`| $\\acute a$\n",
    "`\\bar a`| $\\bar a$\n",
    "`\\breve a` | $\\breve a$\n",
    "`\\ddot a`| $\\ddot a$\n",
    "`\\dot a` | $\\dot a$\n",
    "`\\grave a`| $\\grave a$\n",
    "`\\hat a`| $\\hat a$\n",
    "`\\tilde a` | $\\tilde a$\n",
    "`\\vec a` | $\\vec a$\n",
    "`\\overline{abc}`|$\\overline{abc}$\n",
    "`\\widehat{xyz}`|$\\widehat{xyz}$\n",
    "`\\widetilde{xyz}`|$\\widetilde{xyz}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 特殊字符表"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "参见：http://matplotlib.org/users/mathtext.html#symbols"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 例子"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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uherV/Y7GZJdX89RzuSUMAFVdpqr/CkNMIbOkkb+UFNevkZbmdySJ5ccf4cIL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\noFnSMMYYE7T/Bxi7FV50SWh9AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa567160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "t = np.arange(0.0, 2.0, 0.01)\n",
    "s = np.sin(2*np.pi*t)\n",
    "\n",
    "plt.plot(t,s)\n",
    "plt.title(r'$\\alpha_i > \\beta_i$', fontsize=20)\n",
    "plt.text(1, -0.6, r'$\\sum_{i=0}^\\infty x_i$', fontsize=20)\n",
    "plt.text(0.6, 0.6, r'$\\mathcal{A}\\ \\mathrm{sin}(2 \\omega t)$',\n",
    "         fontsize=20)\n",
    "plt.xlabel('time (s)')\n",
    "plt.ylabel('volts (mV)')\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
